MathDB

Let

n>1

be an integer. Prove that there exists an integer

n-1 \ge m \ge \left \lfloor \frac{n}{2} \right \rfloor

such that the following equation has integer solutions with

a_m>0:

\frac{a_{m}}{m+1}+\frac{a_{m+1}}{m+2}+ \cdots + \frac{a_{n-1}}{n}=\frac{1}{\textrm{lcm}\left ( 1,2, \cdots , n \right )}

Proposed by Navid Safaei

Problem Statement